Lemma 2.1 ([1]}) 
Let \(\Omega \subset {\mathbb {R}}^N\)  be a bounded Lipschitz domain, satisfying the uniform interior sphere condition.
Assume that \(\gamma >2\) , \(\tilde{f}\in L^q(\Omega )\) , for some
\(q\ge \frac{N}{\gamma ^{\prime }}\)  and that
\(u\in W^{1,\gamma }_{\text{loc}}(\Omega )\)  satisfies in a distributional sense
\(-\operatorname{div}(a (x,u,D u)) + |Du|^\gamma \le \tilde{f}\qquad \text{in }\Omega ,\) 
